Introduction to Mathematical StatisticsThe fifth edition of text offers a careful presentation of the probability needed for mathematical statistics and the mathematics of statistical inference. Offering a background for those who wish to go on to study statistical applications or more advanced theory, this text presents a thorough treatment of the mathematics of statistics. |
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Page 359
... statistics Z = n Σa , X , and Y = X ,, a complete sufficient statistic for 9 , n be independent is that Σa , = 0 . 1 1 7.60 . Let X and Y be random variables such that E ( X ) and E ( Y ) # 0 exist for k = 1 , 2 , 3 , . . . . If the ...
... statistics Z = n Σa , X , and Y = X ,, a complete sufficient statistic for 9 , n be independent is that Σa , = 0 . 1 1 7.60 . Let X and Y be random variables such that E ( X ) and E ( Y ) # 0 exist for k = 1 , 2 , 3 , . . . . If the ...
Page 442
... 9 and , if y = 9 , reject H with probability ( using some auxiliary random experiment ) . ( c ) If the loss function is such that L ( { } , } ) = L ( 1 , 1 ) = 0 and L ( 1⁄2 , 1 ) = 1 and ( 1 , 1 ) = 2 show that the minimax procedure is ...
... 9 and , if y = 9 , reject H with probability ( using some auxiliary random experiment ) . ( c ) If the loss function is such that L ( { } , } ) = L ( 1 , 1 ) = 0 and L ( 1⁄2 , 1 ) = 1 and ( 1 , 1 ) = 2 show that the minimax procedure is ...
Page 444
... statistic for 0 . a = ( b ) If α = ẞ , find the sequential probability ratio test of H1 : 0 = 2 against H1 : 0 = 3 . 9.49 . Let X have a Poisson p.d.f. with parameter 0. We shall use a random sample of size n ... Statistical Tests [ Ch . 9.
... statistic for 0 . a = ( b ) If α = ẞ , find the sequential probability ratio test of H1 : 0 = 2 against H1 : 0 = 3 . 9.49 . Let X have a Poisson p.d.f. with parameter 0. We shall use a random sample of size n ... Statistical Tests [ Ch . 9.
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A₁ A₂ Accordingly approximate best critical region C₁ C₂ chi-square distribution complete sufficient statistic conditional p.d.f. confidence interval Consider continuous type converges in probability correlation coefficient critical region defined degrees of freedom denote a random discrete type distribution function F(x distribution with mean distribution with p.d.f. distribution with parameters dx₁ equation Example Exercise Find the p.d.f. gamma distribution given Hint hypothesis H₁ independent random variables integral joint p.d.f. Let the random Let X1 Let Y₁ limiting distribution marginal p.d.f. matrix moment-generating function order statistics P(C₁ p₁ percent confidence interval Poisson distribution positive integer probability density functions probability set function r₁ random experiment random sample respectively sample space Section Show significance level simple hypothesis subset sufficient statistic t-distribution t₂ theorem unbiased estimator variance o² X₁ X₂ Y₁ Y₂ zero elsewhere μ₁ μ₂ σ²